A trader bought two horses for Rs.19,500. He sold one at a loss of 20% and the other at a profit of 15%. If the selling price of each horse is the same, then their cost prices are respectively.

Options

A. Rs.10,000 and Rs.9,500
B. Rs. 11,500 and Rs.8,000
C. Rs.12,000 and Rs.7,500
D. Rs.10,500 and Rs.9,000

Answer

To solve the problem step by step, we will denote the cost prices of the two horses as follows:

Let the cost price of the first horse be \( X \).
Then, the cost price of the second horse will be \( 19500 - X \) (since the total cost price of both horses is Rs. 19,500).

### Step 1: Calculate the Selling Price of the First Horse
The first horse is sold at a loss of 20%.
The selling price (SP) of the first horse can be calculated as:
\[ SP_1 = X - 0.20X = 0.80X \]
Alternatively, this can be expressed as:
\[ SP_1 = \frac{80}{100} \times X = \frac{80X}{100} \]

### Step 2: Calculate the Selling Price of the Second Horse
The second horse is sold at a profit of 15%.
The selling price of the second horse can be calculated as:
\[ SP_2 = (19500 - X) + 0.15(19500 - X) = (19500 - X) \times \frac{115}{100} \]
This can also be expressed as:
\[ SP_2 = \frac{115}{100} \times (19500 - X) \]

### Step 3: Set the Selling Prices Equal
Since the selling prices of both horses are the same, we can set the equations equal to each other:
\[ 0.80X = \frac{115}{100} \times (19500 - X) \]

### Step 4: Clear the Fraction
To eliminate the fraction, we can multiply both sides by 100:
\[ 80X = 115(19500 - X) \]

### Step 5: Expand and Rearrange the Equation
Expanding the right side gives:
\[ 80X = 2235000 - 115X \]
Now, add \( 115X \) to both sides:
\[ 80X + 115X = 2235000 \]
This simplifies to:
\[ 195X = 2235000 \]

### Step 6: Solve for X
Now, divide both sides by 195 to find \( X \):
\[ X = \frac{2235000}{195} = 11400 \]

### Step 7: Calculate the Cost Price of the Second Horse
Now that we have \( X \), we can find the cost price of the second horse:
\[ \text{Cost Price of Second Horse} = 19500 - X = 19500 - 11400 = 8100 \]

### Final Result
Thus, the cost prices of the two horses are:
- Cost Price of the First Horse: Rs. 11400
- Cost Price of the Second Horse: Rs. 8100